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  4. 4.5 g of aluminium (at. mass 27 amu) is deposited at cathode from a molten electrolyte containing Al3+ ions by a certain quantity of electric charge. The volume of hydrogen produced at STP from H+ ions in a solution by the same quantity of electric charge will be

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Q. $4.5\, g$ of aluminium (at. mass $27$ amu) is deposited at cathode from a molten electrolyte containing $Al^{3+}$ ions by a certain quantity of electric charge. The volume of hydrogen produced at STP from $H^+$ ions in a solution by the same quantity of electric charge will be

AIPMTAIPMT 2005Electrochemistry

Solution:

From second law of Faraday
$\frac{m_{ Al }}{m_{ H }} =\frac{E_{ Al }}{E_{ H }} $
$\frac{4.5}{m_{ H }} =\frac{27 / 3}{1}$
or $m_{ H }=0.5 \,g$
$\because$ Volume of $2 \,g \,H _{2}$ at STP $=22.4 \,L$
$\therefore$ Volume of $0.5\, g\, H _{2}$ at STP
$=\frac{22.4 \times 0.5}{2} L =5.6 \,L$